This phase I trial investigates the side effects of brain tumor-specific immune cells (IL13Ralpha2-CAR T cells) in treating patients with leptomeningeal disease from glioblastoma, ependymoma, or medulloblastoma. Immune cells are part of the immune system and help the body fight infections and other diseases. Immune cells can be engineered to destroy brain tumor cells in the laboratory. IL13Ralpha2-CAR T cells is brain tumor specific and can enter and express its genes in immune cells. Giving IL13Ralpha2-CAR T cells may better recognize and destroy brain tumor cells in patients with leptomeningeal disease from glioblastoma, ependymoma or medulloblastoma.

PRIMARY OBJECTIVES:

I. Examine and describe the safety and feasibility of IL13Ralpha2-specific hinge-optimized 41BB-co-stimulatory CAR truncated CD19-expressing autologous T-lymphocytes (IL13Ralpha2-CAR T cells) through intracerebroventricular (ICV) delivery as adjuvant therapy in participants with:

Ia. IL13Ralpha2+ leptomeningeal disease from glioblastoma (arm 1). Ib. IL13Ralpha2+ leptomeningeal disease from ependymoma or medulloblastoma (arm 2).

II. Determine the activity of IL13Ralpha2-CAR T cells based on survival rate at 3 months for both arms.

SECONDARY OBJECTIVES:

I. Describe persistence, expansion and phenotype of endogenous and IL13Ralpha2-CAR CAR T cells in peripheral blood (PB), tumor cyst fluid (TCF) and cerebral spinal fluid (CSF), when available.

II. Describe cytokine levels in PB, TCF, and CSF (when available) over the study period for each arm.

III. Estimate the rate of disease response by Response Assessment in Neuro-Oncology Leptomeningeal Metastases (RANO LM) criteria by study arm where an active response is defined as stable disease or better.

IV. Estimate rate of progression free survival at 3 months by study arm. V. Estimate rate of overall survival (OS) at 3 months by study arm.

VI. In study participants who undergo post therapy biopsy/resection or autopsy:

VIa. Evaluate IL13Ralpha2-CAR T cell persistence in the tumor tissue and the location of the IL13Ralpha2-CAR T cells with respect to the infusion site.

VIb. Evaluate IL13Ralpha2 antigen on tumor tissue pre- and post-CAR T cell therapy.

VII. Use biomathematical modeling of tumor growth to evaluate benefit of treatment.

OUTLINE:

Patients receive IL13Ralpha2-CAR T cells ICV over 5 minutes on day 1. Treatment repeats every 7 days for 4 cycles in the absence of disease progression or unacceptable toxicity. Patients may receive additional cycles per the discretion of the principal investigator.

After completion of study treatment, patients are followed up at 30 days, months 3, 6, 9, 12, and then yearly for up to 15 years.

Inclusion Criteria:

• Participant has verified leptomeningeal metastases
• Participant must have a Karnofsky performance status (KPS) >= 60
• Participant must have a life expectancy of >= 8 weeks
• If participant has a ventriculoperitoneal shunt, the valve must be programmable, and must be able to tolerate their shunts being turned off for 48 hours
• The effects of IL13Ralpha2-CAR T cells on a developing fetus are unknown. For this reason, women of child-bearing potential must have negative serum pregnancy test and agree to use a reliable form of birth control prior to study entry and for at least two months following study treatment. Male research participants must agree to use a reliable form of birth control and not donate sperm during the study and for at least two months following study treatment
• Participant has a histologically confirmed IL13Ralpha2+ tumor expression by immunohistochemistry (IHC) at the initial tumor presentation or recurrent disease (H-score >= 50)
• Participant must have the ability to understand and the willingness to sign a written informed consent
• No known contraindications to leukapheresis, steroids, or tocilizumab

Exclusion Criteria:

• Research participant requires supplemental oxygen to keep saturation greater than 95% and the situation is not expected to resolve within 2 weeks
• Research participant requires dialysis
• Research participant has uncontrolled seizure activity and/or clinically evident progressive encephalopathy
• Failure of research participant to understand the basic elements of the protocol and/or the risks/benefits of participating in this phase 1 study. A legal guardian may substitute for the research participant
• Participant is unwilling to stop treatment with chemotherapy or endocrine therapy and/or radiation one week prior and during the first 4 cycles of the IL13Ralpha2-CAR T cell study
• Shunted participants either have a non-programmable shunt valve, or cannot tolerate their shunts being turned off for 48 hours
• Participant has a coagulopathy or bleeding disorder or cannot safely discontinue anticoagulation prior to placement of a Rickham reservoir
• Participant has a chronic or active viral infection of the central nervous system (CNS)
• Participant has any uncontrolled illness, including ongoing or active infection; participant has known active hepatitis B or C infection; participants with any signs or symptoms of active infection, positive blood cultures or radiological evidence of infections
• Participant is human immunodeficiency virus (HIV) seropositive based on testing performed within 4 weeks of signing the main informed consent
• Participant has an autoimmune disease
• Participant has another active malignancy
• Participant is unable to undergo a brain magnetic resonance imaging (MRI)
• Participant is pregnant or breast feeding. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with IL13Ralpha2-CAR T cells, breastfeeding should be discontinued if the mother wants to participate in this study
• Prospective participants who, in the opinion of the Investigator, may not be able to comply with all study procedures (including compliance issues related to feasibility/logistics)